Since consecutive terms differ by a constant k in this sequence, we have
[tex]a_8 = a_7 + k[/tex]
[tex]a_8 = (a_6+k)+k = a_6+2k[/tex]
[tex]a_8 = (a_5+k)+2k=a_5+3k[/tex]
and so on down to
[tex]a_8 = a_1 + 7k[/tex]
Solve for k :
14 = 49 + 7k ⇒ -35 = 7k ⇒ k = -5
We then do the same as above but in the reverse direction:
[tex]a_9 = a_8+k[/tex]
[tex]a_{10} = a_9+k = a_8+2k[/tex]
[tex]a_{11} = a_{10}+k = a_8+3k[/tex]
and so on, up to
[tex]a_{27} = a_8 + 19k = \boxed{-81}[/tex]
